Course Description: This course provides a working
knowledge of precalculus and its applications.
It begins with a review of algebraic operations . Emphasis is on solving and
graphing equations that involve
linear, polynomial, exponential, and logarithmic functions . Students learn to
graph trigonometric and inverse
trigonometric functions and learn to use the family of trigonometric identities.
Other topics include conic
sections, arithmetic and geometric sequences, and systems of equations.
Course Objectives: After completing this course, students will be able
• Perform operations on real numbers and polynomials.
• Simplify algebraic, rational, and radical expressions .
• Solve linear and quadratic equations and inequalities.
• Solve word problems involving linear and quadratic equations and inequalities.
• Solve polynomial, rational, and radical equations and applications.
• Solve and graph linear, quadratic, absolute value, and piecewise-defined
• Perform operations with functions as well as find composition and inverse
• Graph quadratic, the square root , cubic, and cube root functions.
• Graph and find zeroes of polynomial functions.
• Graph quadratic functions by completing the square, using the vertex formula ,
• Solve and graph exponential and logarithmic equations.
• Express angle measure in degrees or radians.
• Evaluate and simplify trigonometric expressions.
• Know the six trigonometric functions and how to evaluate those trigonometric
positions on the unit circle with respect to the right triangle.
• Graph trigonometric and inverse trigonometric functions.
• Use trigonometric functions to solve a right triangle and apply the Law of
Sines and the Law of
Cosines to solve triangles that are acute or obtuse.
• Solve systems of linear equations and inequalities.
• Model and solve applications using linear systems.
• Evaluate and find partial sums of a series .
• Evaluate and find sums of an arithmetic sequence and a geometric sequence.
• Solve application problems involving arithmetic and geometric sequences and
• Define, identify, and graph conic sections including circle, ellipse,
parabola, and hyperbola.
Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. Precalculus, 6th
edition, McGraw-Hill, 2008.
• Linear Equations and
• Linear Inequalities and
• Absolute Value in
• Solve linear equations by using all
properties of equality and the rules.
• Solve word problems using linear
• Use the notation of inequalities.
• Solve and graph linear inequalities.
• Solve an application using inequalities.
• Solve absolute value equations and
• Solve quadratic equations using the
• Solve word problems involving quadratic
• Solve polynomial equations using the
zero factor property.
• Solve applications using these equation
• Identify and simplify complex numbers.
• Add and subtract complex numbers.
• Multiply and divide complex numbers.
• Solve rational and radical equations.
• Solve quadratic equations using
factoring, the square root property, and
completing the square.
Functions and Graphs
Coordinates and the
Graph of a Line
• Relations, Functions,
• Linear Functions
• Use a table of values to graph linear
• Determine when lines are parallel or
• Use linear graphs in an applied context.
• Identify functions and state their domain
• Use function notation.
• Write a linear equation in function form.
• Use function form to identify the slope .
• Use slope-intercept form to graph linear
• Write a linear equation in point-intercept
• Use these forms to solve applications.
• The Algebra and
• One-to-One and Inverse
• Transformations and
• Compose two functions and find the
• Identify one-to-one functions.
• Find inverse functions using an algebraic method .
• Graph a function and its inverse.
• Use symmetry as an aid to graphing.
• Perform stretches and compressions on
a basic graph.
• Perform vertical and horizontal shifts and
reflections of a basic graph.
• Graph quadratic functions by completing
the square and using transformations.
• Graph a general quadratic function using
the vertex formula.
• Solve applications involving quadratic
• Graph polynomial functions.
• Identify horizontal and vertical
• Use asymptotes to determine the
equation of a rational function from its
• Graph general rational functions.
• Solve applications involving rational
• Find the domain and intercepts of a
Exponential and Logarithmic Functions
• Exponential Functions
• Logarithms and
• The Exponential
Function and Natural
• Evaluate an exponential function.
• Graph exponential functions.
• Solve certain exponential equations.
• Write exponential equations in
• Graph logarithmic functions and find their
• Apply the properties of logarithms.
• Evaluate and graph the natural logarithm and exponential functions.
• Solve applications of logarithmic and
Exponential and Logarithmic Equations
• Exponential Equations
• Logarithmic Equations
• Applications of
• Write logarithmic and exponential
equations in simplified form.
• Solve exponential equations.
• Solve logarithmic equations.
• Solve applications involving exponential
and logarithmic equations.
• Use exponential equations to find the
interest compounded n times per year.
• Use exponential equations to find the
interest compounded continuously.
An Introduction to Trigonometric
• Special Angles and the
• Graphs of Basic
• Applications of Basic
• Correctly use vocabulary associated with
a study of angles and triangles.
• Convert between degrees and radians for nonstandard angles.
• Define the six trigonometric functions in
terms of a point on the unit circle or in
terms of a real number.
• Identify and discuss important
characteristics of tangent and cotangent.
• Solve applications of trigonometric
• Find values of the six trigonometric
functions from their ratio definition.
• Graph the basic trigonometric functions.
• Transformations and
• Family of Trigonometric
• The Inverse
and Their Applications
• Use fundamental identities to express a
given trigonometric function in terms of
the other five.
• Solve applications using these identities.
• Find the inverse trigonometric functions
and evaluate related expressions.
• Apply the definition and notation of inverse trigonometric functions
• Graph sine and cosine functions with
various amplitudes and periods.
• Write the equation for a given graph.
• The Law of Sines
• The Law of Cosines
• More Applications of
• Solve ASA and AAS triangles.
• Use the Law of Sines to solve
• Apply the Law of Cosines when two sides
and an included angle are known (SAS).
• Apply the Law of Cosines when three
sides are known (SSS).
• Solve applications using the Law of
• Solve more applications involving trigonometric functions.
• Solve the SSA case, including the
• Solving Systems
Substitution, and Using
• Solving Linear Systems
Using Matrix Equations
• Applications of Linear Systems
• Solve linear systems by graphing, by
substitution, and by elimination.
• Use system of equations to mathematically model and solve
• Form the augmented matrix of a system
• Solve a system of equations using row operations.
• Recognize inconsistent and dependent systems.
• Use system of equations to
mathematically model and solve
• Define and identify a parabola.
• Graph a parabola.
• Solve applications of parabolas.
• Define and identify an ellipse and a
• Graph an ellipse and a circle.
• Solve applications of ellipses and circles.
• Define and identify a hyperbola.
• Graph a hyperbola.
• Solve applications of hyperbolas
Sequences and Series
• Sequences and Series
• Arithmetic Sequences
• Geometric Sequences
• Write the terms of a sequence given the
• Determine the general term of a
• Find the partial sum of a series.
• Use summation notation to write and
• Solve applications involving arithmetic
• Find the sum of a geometric series.
• Solve application problems involving
geometric sequences and series.